First-order classification, non-standard models, and interpretations

In this talk I will focus on three things:
1. First-order classification: in particular, how one can describe ALL groups which are first-order equivalent to a given one.
2. Non-standard models of groups: in particular, I will describe non-standard models of the finitely generated groups with decidable or recursively enumerable (or arithmetic) word problems and explain how they naturally appear as non-standard Z-points of the general algebraic schemes.
3. Theory of interpretations: it seems a new rich theory is emerging right now. I will show several interesting results based on interpretations.